A formalism of semiclassical asymptotics has been developed for a two-component Hartree-type evolutionary equation with a small asymptotic parameter multiplying the partial derivatives, a nonlocal cubic nonlinearity, and a Hermite matrix operator. Semiclassical solutions are constructed in the class of two-component functions concentrated in the neighborhood of a point moving along the phase trajectory of a dynamic Hamilton–Ehrenfest system.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–66, October, 2009.
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Smirnova, E.I., Trifonov, A.Y. & Shapovalov, A.V. Formalism of semiclassical asymptotics for a two-component Hartree-type equation. Russ Phys J 52, 1068–1076 (2009). https://doi.org/10.1007/s11182-010-9340-2
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DOI: https://doi.org/10.1007/s11182-010-9340-2